Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this method when the gradients are sampled from Markov processes, and hence biased and dependent from time step to time step; in contrast, the analysis in existing work relies heavily on the stochastic gradients being independent and sometimes unbiased. Our main contributions show that under certain (standard) assumptions on the underlying Markov chain generating the gradients, ASGD converges at the nearly the same rate with Markovian gradient samples as with independent gradient samples. The only difference is a logarithmic factor that accounts for the mixing time of the Markov chain. One of the key motivations for this study are complicated control problems that can be modeled by a Markov decision process and solved using reinforcement learning. We apply the accelerated method to several challenging problems in the OpenAI Gym and Mujoco, and show that acceleration can significantly improve the performance of the classic temporal difference learning and REINFORCE algorithms.
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